SOLUTION: Find {{{ f^-1 }}}(x) in each case... f(x) = {{{ e^(x-3) }}} + 2 f(x) = {{{ log3(2x+1) }}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find {{{ f^-1 }}}(x) in each case... f(x) = {{{ e^(x-3) }}} + 2 f(x) = {{{ log3(2x+1) }}}      Log On


   

Question 193667: Find +f%5E-1+(x) in each case...

f(x) = +e%5E%28x-3%29+ + 2

f(x) = +log3%282x%2B1%29+
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
inverse is by definition the reflection of a function over the line y=x.
The simple method of changing a function is to interchange x for y, and y for x.
1) f(x)=y=e^(x-2) + 2
inverse is x=e^(y-2)+2
normally the inverse is simplified to y=function
x-2=e^(y-2)
taking ln of both sides
ln(x-2)=(y-2)
ln(x-2)+2=y ANSWER
2) y=log base 3 (2x+1)
inverse is
x = log base 3 (2y+1)
raising both sides to powers of 3
3^x=2y+1
3^x-1=2y
(3^x-1)/2 = y ANSWER